South Korea is consulting with the United States on the rotational deployment of strategic U.S. military assets around the Korean Peninsula, Cheong Wa Dae said Thursday.

"The deployment could begin before the end of the year or after the new year," a presidential aide told reporters.

He said the timing was flexible depending on how the consultation goes, adding, "Consultations about the details are ongoing."

The statement came a day after President Moon Jae-in's top security advisor said the U.S. will deploy strategic weapons around the peninsula on a rotational basis as early as late this year.

Chung Eui-young, the chief of the National Security Office, made the remarks during the President's meeting with the leaders of four political parties at Cheong Wa Dae, according to Rep. Cheong Yang-seog, deputy floor leader of the conservative opposition Bareun Party.

"The United States has pledged to expand the rotational deployment of its strategic assets near the peninsula," Chung told the party leaders when asked if there were "any cracks" between Seoul and Washington.

"The deployment will begin as early as the end of the year and will contribute to strengthening our defensive capabilities," he said.

Some critics are calling Washington's security commitment into question amid the Kim Jong-un regime's push to develop a nuclear-armed intercontinental ballistic missile capable of striking targets on the U.S. mainland. They say this may make the U.S. reluctant to defend its Asian ally and follow its own path without consulting with Seoul.

The security advisor did not specify which assets could be deployed. U.S. strategic weapons usually refer to heavy bombers, nuclear-powered aircraft carriers and submarines as well as stealth fighters.

Rep. Park Wan-joo, the spokesman of the ruling Democratic Party of Korea, quoted Cheong Wa Dae as saying that Washington has given its pledge on the deployment in writing.

During his visit to New York to attend the U.N. General Assembly last week, President Moon reached an agreement with his U.S. counterpart Donald Trump to expand the rotational deployment of the U.S. key military assets to the peninsula and its surrounding area. At the time, the two heads of state did not mention a detailed timeline for this.

For its part, the Ministry of National Defense also said Seoul and Washington are in close consultation on the issue, considering the grave security situation on the peninsula.

"The two nations are making efforts to conclude the consultations at the earliest possible date," said Col. Lee Jin-woo, deputy spokesman for the defense ministry.

Pentagon spokesman Lt. Col. Christopher Logan said the two allies are working to find the best way to implement a plan on the deployment, according to Voice of America. The spokesman refused to elaborate on the details.

Military tension on the peninsula has been escalating amid a war of words between Washington and Pyongyang.

The U.S. president threatened to "totally destroy" the North if the U.S. is forced to defend itself or its allies, and then flew B-1B bombers from Guam and F-15 fighters from Okinawa farther north of the Demilitarized Zone (DMZ) than any American warplanes have flown in the 21st century, Saturday.

In response, North Korean Foreign Minister Ri Yong-ho said Monday his country would shoot down U.S. bombers if necessary as it has "every right to take all self-defensive countermeasures."